STA2023 QUIZ 6

Q1

What is the relationship between the linear correlation coefficient r and the slope b1​ of a regression line?

Choose the correct answer below:

A. The value of r will always be larger than the value of b1​.

B. The value of r will always be smaller than the value of b1​.

C. The value of r will always have the opposite sign of the value of b1​.

D. The value of r will always have the same sign as the value of b1​.

Q2

Assume that when human resource managers are randomly selected, 41% say job applicants should follow up within two weeks. If 5 human resource managers are randomly selected, find the probability that exactly 3 of them say job applicants should follow up within two weeks.

The probability is _____. (Round to four decimal places as needed.)

Q3

Listed below are annual data for various years. The data are weights (metric tons) of imported lemons and car crash fatality rates per 100,000 population. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using α=0.05. Is there sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality rates? Do the results suggest that imported lemons cause car fatalities?

The linear correlation coefficient r is _____. (Round to three decimal places as needed.)

There is/is not sufficient evidence to support the claim that there is a linear correlation between lemon imports and crash fatality rates for a significance level of α=0.05.

Do the results suggest that imported lemons cause car fatalities?

• A. The results suggest that imported lemons cause car fatalities.
• B. The results suggest that an increase in imported lemons causes car fatality rates to remain the same.
• C. The results do not suggest any cause-effect relationship between the two variables.
• D. The results suggest that an increase in imported lemons causes an increase in car fatality rates.

What are the null and alternative hypotheses?

• A. H0:ρ=0, H1:ρ<0
• B. H0:ρ=0, H1:ρ≠0
• C. H0:ρ=0, H1:ρ>0
• D. H0:ρ≠0, H1:ρ=0

Construct a scatterplot. Choose the correct graph below.

Q4

A data set includes data from student evaluations of courses. The summary statistics are n=86, xˉ=3.41, s=0.57. Use a 0.05 significance level to test the claim that the mean of the population of student course evaluations is equal to 3.50. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

What are the null and alternative hypotheses?

   A. H0:μ=3.50, H1:μ<3.50

   B. H0:μ=3.50, H1:μ>3.50

   C. H0:μ=3.50, H1:μ≠3.50

   D. H0:μ≠3.50, H1:μ=3.50

Determine the test statistic.

__________ (Round to two decimal places as needed.)

Determine the P-value.

__________ (Round to three decimal places as needed.)

State the final conclusion that addresses the original claim.

Q5

Assume a significance level of α=0.05 and use the given information to complete parts (a) and (b) below.

Original claim: Less than 45% of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of 0.0431.

a. State a conclusion about the null hypothesis. (Reject H0H0​ or fail to reject H0​.) Choose the correct answer below.

   A. Reject H0​ because the P-value is less than or equal to α.

   B. Reject H0 because the P-value is greater than α.

   C. Fail to reject H0 because the P-value is greater than α.

   D. Fail to reject H0​ because the P-value is less than or equal to α.

b. Without using technical terms, state a final conclusion that addresses the original claim. Which of the following is the correct conclusion?

A. The percentage of adults that would erase all of their personal information online if they could is more than or equal to 45%.

B. There is not sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information online if they could is less than 45%.

C. There is sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information online if they could is less than 45%.

D. The percentage of adults that would erase all of their personal information online if they could is less than 45%.

Q6

mong fatal plane crashes that occurred during the past 60 years, 237 were due to pilot error, 67 were due to other human error, 434 were due to weather, 100 were due to mechanical problems, and 262 were due to sabotage.

a. Construct the relative frequency distribution. Complete the relative frequency distribution below. (Round to one decimal place as needed.)

b. What is the most serious threat to aviation safety, and can anything be done about it? Choose the correct answer below.

• A. Pilot error is the most serious threat to aviation safety. Pilots could be better trained.
• B. Mechanical problems are the most serious threat to aviation safety. New planes could be better engineered.
• C. Sabotage is the most serious threat to aviation safety. Airport security could be increased.
• D. Weather is the most serious threat to aviation safety. Weather monitoring systems could be improved

Q7

Assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a standard deviation of 1.

Draw a graph and find P15P15​, the 15th percentile. This is the bone density score separating the bottom 15% from the top 85%.

Which graph represents P15​? Choose the correct graph below.

The bone density score corresponding to P15​ is _____ (Round to two decimal places as needed.)

Q8

In a study involving high school students aged 16 years and above, researchers aim to determine if there is a relationship between two risky behaviors: texting while driving and driving under the influence of alcohol. The researchers collected survey data summarized in the table below. Using a significance level of 0.05, test the claim that these two risky behaviors are independent.

Determine the null and alternative hypotheses:

• H0​: There is no association between texting while driving and driving under the influence of alcohol (the behaviors are independent).
• H1: There is an association between texting while driving and driving under the influence of alcohol (the behaviors are not independent).

Calculate the chi-square test statistic using the data provided (round to two decimal places)

Determine the p-value corresponding to the test statistic (round to three decimal places).

Based on the p-value, conclude whether to reject or fail to reject the null hypothesis at the 0.05 significance level.

State whether the data suggests a relationship between the two risky behaviors.

Q9

The following data represents the number of hurricanes that occurred in each year in a certain region. The data is listed in order by year:

2,10,10,20,17,17,10,13,17,18,9,15,13,10,18,10

Calculate the following measures of variation for the sample data:

• The range of the sample data (round to one decimal place).
• The standard deviation of the sample data (round to one decimal place).
• The variance of the sample data (round to one decimal place).

What important feature of the data is not revealed through the different measures of variation?

A. The measures of variation do not reveal the difference between the largest number of hurricanes and the smallest number of hurricanes in the data.

B. The measures of variation reveal nothing about how the numbers of hurricanes are spread.

C. The measures of variation reveal nothing about the pattern over time.

D. The measures of variation reveal no information about the scale of the data.

Q10

The histogram displayed represents the weights (in pounds) of members of a high school debate team.

Determine the total number of team members represented in the histogram.

Options:

The histogram represents [ ] debate team members.

Q11

The random variable X represents the number of color television sets owned by a randomly selected household with an annual income between $15,000 and $29,999. The probability distribution of X is given below:

Find the expected value E(X) for the random variable X.

Round your answer to three decimal places as needed.

Q12

Consider the following scenarios and determine the probabilities:

Find the probability that when a single six-sided die is rolled, the outcome is 1.

(Round your answer to three decimal places as needed.)

Find the probability that when a coin is tossed, the result is tails.

(Round your answer to three decimal places as needed.)

Find the probability that when a six-sided die is rolled, the outcome is 18.

(Round your answer to three decimal places as needed.)

Q13

The table below shows the drive-thru order accuracy at four popular fast-food chains. The data lists the number of orders that were accurate and those that were not:

Assume that one order is randomly selected from the data.

Calculate the probability that the selected order is not accurate.

(Round your answer to three decimal places as needed.)

Q14

Assume that adult IQ scores are normally distributed with a mean of 101.8 and a standard deviation of 22.5.

Find the probability that a randomly selected adult from this group has an IQ greater than 134.1.

Hint: Draw a graph to help visualize the problem.

Round your answer to four decimal places as needed.

Q15

Given in the table are the BMI statistics for random samples of men and women. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal.

Use a 0.05 significance level to test the claim that males and females have the same mean body mass index (BMI).

What are the null and alternative hypotheses?

A. H0:μ1=μ2, H1:μ1>μ2

B. H0:μ1≠μ2H, H1:μ1<μ2

C. H0:μ1≥μ2 ​, H1:μ1<μ2

D. H0:μ1=μ2 ​, H1:μ1≠μ2

Calculate the test statistic t (round to two decimal places as needed).

Determine the P-value corresponding to the test statistic (round to three decimal places as needed).

State the conclusion for the test:

A. Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

B. Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

C. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

D. Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

Q16

Researchers collected data on the number of hospital admissions resulting from motor vehicle crashes. The results are given below for Fridays on the 6th of a month and Fridays on the following 13th of the same month. Use a 0.05 significance level to test the claim that when the 13th day of a month falls on a Friday, the numbers of hospital admissions from motor vehicle crashes are not affected.

State the hypotheses for this test:

Let μd be the mean of the differences in the numbers of hospital admissions.

H0:μd__0

H1:μd__0

Find the value of the test statistic tt (round to three decimal places as needed).

State the result of the test:

A. There is sufficient evidence to warrant rejection of the claim of no effect. Hospital admissions do not appear to be affected.

B. There is not sufficient evidence to warrant rejection of the claim of no effect. Hospital admissions appear to be affected.

C. There is sufficient evidence to warrant rejection of the claim of no effect. Hospital admissions appear to be affected.

D. There is not sufficient evidence to warrant rejection of the claim of no effect. Hospital admissions do not appear to be affected.

Q17